vessel is full of 90ltr milk, 18ltr milk is taken out and replaced by water and again this process is repeated 2 times, the amount of milk left after the 3rd replacement is?

Options

A. 11.52 ltr
B. 46.08 ltr
C. 23.04 ltr
D. 69.12 ltr

Answer

To solve the problem step by step, we will calculate the amount of milk left in the vessel after each replacement of milk with water.

**Step 1: Initial Setup**
- The vessel initially contains 90 liters of milk.

**Step 2: First Replacement**
- We take out 18 liters of milk.
- Amount of milk left after taking out 18 liters = 90 liters - 18 liters = 72 liters.
- We then add 18 liters of water to the vessel, so the total volume remains 90 liters (72 liters of milk + 18 liters of water).

**Step 3: Calculate the proportion of milk left after the first replacement**
- The proportion of milk left after the first replacement = (Amount of milk left) / (Total volume) = 72 liters / 90 liters = 4/5.
- Thus, after the first replacement, the amount of milk left = 90 liters * (4/5) = 72 liters.

**Step 4: Second Replacement**
- Again, we take out 18 liters of the mixture (which now contains both milk and water).
- The amount of milk in the 18 liters taken out = (72 liters of milk / 90 liters total) * 18 liters = 14.4 liters.
- Therefore, the amount of milk left after the second replacement = 72 liters - 14.4 liters = 57.6 liters.
- We add 18 liters of water again, so the total volume remains 90 liters (57.6 liters of milk + 32.4 liters of water).

**Step 5: Calculate the proportion of milk left after the second replacement**
- The proportion of milk left after the second replacement = 57.6 liters / 90 liters = 64/100 = 16/25.
- Thus, after the second replacement, the amount of milk left = 90 liters * (16/25) = 57.6 liters.

**Step 6: Third Replacement**
- We take out 18 liters of the mixture again.
- The amount of milk in the 18 liters taken out = (57.6 liters of milk / 90 liters total) * 18 liters = 13.76 liters.
- Therefore, the amount of milk left after the third replacement = 57.6 liters - 13.76 liters = 43.84 liters.
- We add 18 liters of water again, so the total volume remains 90 liters (43.84 liters of milk + 46.16 liters of water).

**Step 7: Final Calculation**
- The amount of milk left after the third replacement is 43.84 liters.

**Final Answer:**
The amount of milk left after the 3rd replacement is **43.84 liters**.

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